Most programs will guide you to take each test on "their schedule". It
looks bad for them if their residents fail.
Anyway, the ABR (
www.theabr.org):
Candidates will be considered for the Physics portion of the written examination only when they have completed 12 months of diagnostic radiology training. After 24 months of diagnostic radiology training, candidates will be considered for the Clinical portion of the written examination.
A candidate who has passed the cognitive examination and will have completed 60 months of approved training by September 30 in the year in which the exam is given will be considered for the oral examination. Admissibility to the oral examination is determined by the ABR Executive Committee.
-----------
Therefore, unless they make exceptions, you don't have much choice.
Unless you have special training or an unusual background, sitting for the oral boards before the end of residency seems unrealistic. A large part of your last year will be tailored to getting you ready for the orals. Most programs have extra sessions, give you less call, etc. The oral boards are the most intense test you will ever take (unless you go on to CAQs). I wouldn't rush it.